0=2x^2+2x-84

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Solution for 0=2x^2+2x-84 equation: 


Simplifying
0 = 2x2 + 2x + -84

Reorder the terms:
0 = -84 + 2x + 2x2

Solving
0 = -84 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 84 = 84
84 + -2x + -2x2 = -84 + 2x + 2x2 + 84 + -2x + -2x2

Reorder the terms:
84 + -2x + -2x2 = -84 + 84 + 2x + -2x + 2x2 + -2x2

Combine like terms: -84 + 84 = 0
84 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
84 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
84 + -2x + -2x2 = 0 + 2x2 + -2x2
84 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
84 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -1x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(7 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {6, -7}

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